Do women pray Friday Prayer or Dhuhr Prayer, and should their prayer be individually or in congregation, and how do they complete their prayer if they catch one rak'ah of Friday Prayer with the Imam and the sound cuts off?

If women witness the Friday prayer in the mosque and enter into the state of ihram for it with the Imam, then they pray Jumu'ah, not Dhuhr, and it is forbidden for them to interrupt it. If they separate from the Imam due to an excuse, they complete it as Jumu'ah if they have caught one rak'ah with him. At that point, they have the choice between one of them leading the prayer to complete it in congregation, or each one completing her prayer individually.